Question

manuel deposits $10000 for 12 yr in an account paying 4% compounded annually.He then puts this total amount on deposit in another account paying 5% compounded semiannually for another 9yr. Find the total amount on deposit after the entire 14 yr period.

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$10000\\ r=rate\to 4\%\to (4)/(100)\to &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &12 \end{cases} \\\\\\ A=10000\left(1+(0.04)/(1)\right)^(1\cdot 12)\implies A=1000(1.04)^(12)\\\\\\ A\approx 16010.32`

he then turns around and grabs that money and sticks it for another 9 years,


`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) ~~ \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$16010.32\\ r=rate\to 5\%\to (5)/(100)\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2\\ t=years\to &9 \end{cases} \\\\\\ A=16010.32\left(1+(0.05)/(2)\right)^(2\cdot 9)\implies A=16010.32(1.025)^(18) \\\\\\ A\approx 24970.64`

add both amounts, and that's how much is for the whole 21 years.